Cremona's table of elliptic curves

2352 = 2⁴ · 3 · 7²

Field	Data	Notes
Atkin-Lehner	2- 3- 7+	Signs for the Atkin-Lehner involutions
Class	2352r	Isogeny class
Conductor	2352	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	-141675749376 = -1 · 213 · 3 · 78	Discriminant
Eigenvalues	2- 3-  1 7+ -5  0 -4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-800,-20364]	[a1,a2,a3,a4,a6]
Generators	[114:1176:1]	Generators of the group modulo torsion
j	-2401/6	j-invariant
L	3.7316897839152	L(r)(E,1)/r!
Ω	0.41804097115226	Real period
R	0.74388438004641	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	294a1 9408bp1 7056bk1 58800fa1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2352r1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	1	+	-5	0	-4	-8	4	-5	-3	-4	0	-2	6	-9	11	-6	2	-2	10	-3	7	-6	7

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Quadratic twists for elliptic curve 2352r1

-4	8	-3	5	-7
294a1	9408bp1	7056bk1	58800fa1	2352l1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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